Introduction

Groundwater levels are fundamental to the practice of hydrogeology. They are necessary for flow system analysis and understanding (e.g., determining hydraulic gradients, provide calibration targets for 3D numerical models), and applying this understanding to water resource management. From a hydrological perspective, knowledge of water table depths and their seasonal fluctuation is also vital when constructing and maintaining underground infrastructure (e.g., sewers, water mains) and when siting LIDs.

The Oak Ridges Moraine Groundwater Program is a municipal agency charged with synthesizing and disseminating water resources data, geologic interpretations, and numerical models over a 30,000 km² area situated in south-central Ontario. One of our interpretive mapping products gaining increased use are estimations of the depth to water tables. These maps are constructed from thousands of data points considered to represent an average condition. An effective use of these maps must consider i) longer-term deviation from these “average” conditions, and ii) water table sensitivity to storm and/or snow melt events.

Numerous active monitoring wells exist within the study area, collecting regular (e.g., daily, hourly, or less) groundwater level data over many years. When evaluated alongside climate data (e.g., precipitation and snow melt estimations) the hydrogeological response to events or stresses is apparent. Long-term seasonal variability in shallow groundwater level has been quantified using a 12-point Generalized Additive Model that provides confidence intervals to a fitted seasonal trend. From 656 shallow wells, the southern Ontario water table fluctuates ±86 (s.d. 81) cm, that is, the range extended by the 90th confidence interval.


Pattern + Noise

The intention is to determine the variability/error one should expect when reading our interpolated water table map. The water table map should be though of as a long-term average with uncertainty associated with the when (in the past century) the measurements were made. It is a surface interpolated from 100,000s measurements and constrained with mapped watercourses.

In reality, the depth to water table varies seasonally in the order of 1m. Long-term trends in water levels and aquifer storage further impacts expected water levels.

Total expected variability is assumed described by 2 components: seasonal variability + inter-annual variability.

  1. seasonal variability is modelled using a statistical model (below); and
  2. inter-annual variability is assessed by the confidence intervals from the statistical model.

Methodology

Generalized Additive Model

The Generalized Additive Model (GAM) is a flexible means of fitting a model to time series data. It is a generalization of the linear models we’ve all fitted to point data, which means it retains the ability to efficiently compute confidence/prediction intervals intuitive control (Wood, 2017).

GAMs are especially useful as hydrographs contain a good deal of noisy auto-correlated data (that is, a sequence of measurements made in a short time frame tend to be correlated). For instance, it’s apparent that there is a seasonal pattern to most hydrological data in southern Ontario, there the GAM designed with 12 smoothing spline “knots”, one for every calendar month. These monthly knots are further specified as being a cyclic regression spline by assuring that the surface remains continuous to the second derivative at a years end (Wood, 2017).

processing steps

Of the 985 locations with >34 water level logger measurements are queried from our database. Of these, data were screened for having a reported well screen depth and had at least 5 years of data. Interested only in Shallow well (defined here as wells <20m deep), 690 wells remained. In addition, for every location timeseries:

  1. water level data were re-sampled to daily averages
  2. outliers were automatically removed using the ±1.5IQR (inter-quartile range) method
  3. monitoring locations with less than 34 records where removed
  4. monitoring locations with less than a 4 year period of record where removed
  5. monitoring locations without a reported depth where removed
  6. values are factored according to their day-of-year and year of the reported level

values are fitted to a Generalized additive mixed model (GAMM), using 12 (monthly) + n years degrees of freedom:

\[ \texttt{h}_i = f_\tilde{m}(\texttt{day.of.year}_i) + f_{yr}(\texttt{year}_i) + e_i, \quad e_i=\phi e_{i-1}+\epsilon_i \]

\(\tilde{f}_1\) seasonal variability is taken as the amplitude of the GAM, \(e_i\) is the AR(1) autocorrelation function.

See GAM plots of all locations here.

Maps

Maps of variability

click on any circle to reveal station properties. Full-screen available in the top-left corner

Shallow (<20m) wells

Deep (<20m) wells

Maps of trend

click on any triangle to reveal station properties. Full-screen available in the top-left corner

Shallow (<20m) wells

Deep (<20m) wells

References

Wood, S.N., 2017. Generalized Additive Models: An introduction with R, 2nd ed. CRC Press. 476pp.